Depending on who you ask, Russian President Vladimir Putin, right, will find it easy to take advantage of Donald Trump’s inexperience — or Trump will use his dealmaking skills to improve U.S.-Russia ties. (Michael Klimentyev /Pool via European Pressphoto Agency)

For much of this year, Donald Trump and Vladi­mir Putin have been engaged in a long-distance courtship. They have said kind things about each other in public and separately expressed visions of a mutually agreeable future.

Since Trump’s election, the anticipation has become more explicit. It culminated this week in the U.S. president-elect’s call for America to “move on” from allegations of Russian electoral hacking, and the Russian president’s blithe pronouncement Friday that he would rather plan for a new relationship with Trump than retaliate in kind to sanctions and expulsions ordered by outgoing President Obama.

But as with all such arms-length pairings, the looming question is whether Trump and Putin will find fulfillment or disappointment once face-to-face reality strikes.

U.S. and Russian officials and experts are deeply divided over the answer. Some see Moscow playing Trump like a fiddle. The Kremlin “sees Trump’s presidency as a net loss for the U.S. strategic position that Russia should take advantage of,” said Vladi­mir Frolov, a Moscow-based analyst.

(Bastien Inzaurralde/The Washington Post)

Others depict the Russians as genuinely willing to deal and cautiously optimistic about improved relations under a U.S. president who has none of the prejudices they see in the Obama administration.

While some fear that Trump has no firm understanding of the policy complications ahead and the threats posed by Russia, others say Trump the dealmaker may be just the right person to set relations back on a road to cooperation that will benefit U.S. national security.

Trump has identified areas of shared U.S.-Russia interests, including counterterrorism in general — and rolling back the Islamic State in particular — as well as countering nuclear weapons proliferation. He has suggested that there are deals to be struck with Moscow on Syria and Ukraine, indicated that NATO’s strong defensive posture on Russia’s western border may be negotiable, expressed skepticism about sanctions — unless applied to Iran or North Korea — and implied that the fuss over Russian electoral hacking is overblown.

Some of his pronouncements have huge policy gaps and contradictions. In Syria, for example, how would counterterrorism cooperation with Russia against the Islamic State influence Trump’s plans to crack down on Russian ally Iran, which has its own interests in both Syria and Iraq?

The first indication of policy substance may come two weeks from now, when Trump’s nominee for secretary of state, Rex Tillerson — the ExxonMobil chief executive who has argued that sanctions against Russia hurt U.S. business — appears before the Senate Foreign Relations Committee. Several Republican lawmakers, including committee Chairman Bob Corker (Tenn.), have said that any move to begin a new relationship with Russia by diluting or removing Ukraine-related sanctions is a nonstarter.

Putin and his advisers have spoken about a desire to improve relations, although there is no Kremlin expectation that Inauguration Day will bring an overnight change. While pleased by the direction in which Trump appears to be moving, Moscow sees “policy incoherence” so far from the president-elect, said Thomas Graham, who served as senior Russia director on George W. Bush’s National Security Council staff and is now managing director at Kissinger Associates.

“If I read what the Russians have been saying, they don’t expect relations to turn around quickly,” Graham said in an interview. “They’re surprised that on the Western side it’s seen as if President Trump is going to hand over the keys to the barn to Russians.”

But however disjointed and contradictory his shorthand policy prescriptions have seemed so far, “the vision in the Kremlin is that even though Trump is a novice in foreign policy, he has a record of striking deals that benefit him, as well as a team of experienced advisers,” said Maxim A. Suchkov, an analyst at the Russian International Affairs Council, a Moscow think tank.

Some Russian experts said the Kremlin realizes that if Trump moves too fast — especially in the wake of the hacking scandal — it would probably cause strong pushback from Congress and elsewhere. Instead, they see Putin’s most recent actions as part of the pre-inauguration theater, preparing the ground for a hoped-for, but still uncertain, future.

“Putin will play this as Obama acting like a deranged and spiteful madman, while Trump is a real gentleman who needs to be treated like a gent by Russia,” Frolov said of Putin’s low-key response to the sanctions and expulsions. The Russian president “does not want to do anything that would make it even harder for Trump to move positively on Russia,” he said.

Others detected a more nefarious strategy at work in Putin’s gambit. “I think it’s brilliant,” said Steve Hall, who ran Russia operations for the CIA before his retirement in 2015. “It solidifies the relationship and plays straight to Trump’s ego. It allows Trump to say, ‘See, the Obama administration is behaving childishly, and we need to act much more professionally.’ ”

Putin, Hall said, is also probably maneuvering to gain maximum leverage over an incoming president whose constant touting of himself as a dealmaker makes him need a deal more than Moscow does. Now, he said, Putin can greet the new president by saying: “You still owe me one. I can pull that back and make you look like you’re not the great negotiator you say you are.”

Despite differences on how to deal with individual conflicts, think tanks across Washington have advised Trump to end the Obama-era policy of not talking to the Kremlin and to begin a new, across-the-board dialogue.

On its own, “dialogue won’t be enough in and of itself over time,” Andrew C. Kuchins, a senior fellow and research professor at the Center for Eurasian, Russian and East European Studies, said in an interview. “The Trump folks would make a huge mistake if they unilaterally repealed sanctions. Congress would re-legislate them, creating a Jackson-Vanik situation,” he said, referring to the 1974 law that restricted the president’s ability to trade with Soviet Bloc countries that restricted human rights.

After interviewing policymakers and experts in this country and in Russia, Kuchins this month issued a lengthy report for the Center on Global Interests, recommending an elevation of the U.S.-Russia relationship to the presidential level “as incentive for Moscow to adjust and accommodate,” and a bilateral renewal of dialogue on a range of issues, from arms control and terrorism to cybersecurity. At the same time, he wrote, a “calibrated” approach must include a firm U.S. commitment to NATO allies and the continuation of a credible deterrent against Russian encroachments in Eastern Europe.

“This is not a call for a ‘reset’ or a ‘strategic partnership,’ ” Ku­chins wrote, “but a reevaluation of the excessive risks the United States is running with the current downward trajectory of U.S.-Russia relations. Containment or deterrence alone cannot mitigate these risks.”

Mark Dubowitz, executive director of the Foundation for Defense of Democracies, while emphasizing that he did not necessarily support it, outlined a possible play for Trump that would combine several policy priorities. “You could see a Trump administration potentially diminishing or suspending U.S. sanctions on Russia, working with the Europeans, recognizing the de facto annexation of Crimea, and making clear the United States is not going to permit Ukraine to join NATO or the European Union. It would be a signal to Putin that NATO expansion has stopped.

“But at the same time,” Dubowitz said, “in exchange for what are significant concessions to Putin, you get agreement to roll back Iranian influence in Syria and to make changes” to the Iran nuclear deal, which both the United States and Russia negotiated.

Overall, experts stressed the need for transparency and communication on a range of issues that are now at a stalemate.

“We don’t want this to spin out of control. We need to have conversations to understand what people are doing so that we don’t misread each other,” said Graham, who declined to comment on media reports that he is under consideration as Trump’s ambassador to Moscow.

The question, Graham said, is whether Trump has the patience to take his time. “Will Trump understand that negotiations with Russia need to be from a position of strength? That means he needs to have the allies behind him. Are you, Trump, so enamored with Putin that you decide first thing you need to sit down and have a conversation, or do you do it the way other presidents did?

“Are you going to see him at the end of a European trip, where you talk to the allies first and make sure you have a common understanding of the challenge, a common understanding of how you’re going to deal with it? To then say: ‘We’re now going to sit down with you, Mr. Putin. . . . We’re prepared to take your interests into account, but you also need to take our interests into account.’ ”

“I actually think the Russians may not expect that,” Graham said. “But they would respect it and be able to deal with it.”

Filipov reported from Moscow. Greg Miller, Karoun Demirjian and Robert Costa in Washington contributed to this report.